1. Field of the Invention
The present invention relates to radio-wave direction-of-arrival tracking methods and their apparatuses. In particular, the present invention relates to a direction-of-arrival tracking method and apparatus for estimating the directions-of-arrival of radio waves received by an adaptive array antenna.
2. Description of the Related Art
There have been recent interests in the research and development of mobile communication systems using an adaptive array antenna. A typical array antenna includes a plurality of antenna elements arranged in different spatial locations such that the outline of the antenna elements has a certain geometry shape. A technique for estimating the directions-of-arrival of radio waves (hereinafter, a radio wave may be referred to as a signal from the viewpoint of signal processing) impinging on an array antenna is one of the most important fundamental technologies associated with adaptive array antennas.
Subspace-based methods are well-known approaches to the issue of estimating the directions-of-arrival of signals because of its estimation accuracy and computational load, where the orthogonality between the signal subspace and the noise subspace is exploited. The multiple signal classification (MUSIC) technique is a typical one of subspace-based methods (refer to, for example, R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas and Propagation, vol. 34, no. 3, pp. 276–280 (1986)). The subspace-based method with spatial smoothing is also well known as an approach to estimate the directions-of-arrival of coherent signals with full correlation. A typical example of the subspace-based method with spatial smoothing is the spatial smoothing based MUSIC technique (refer to, for example, T. J. Shan, M. Wax and T. Kailath, “On spatial smoothing for direction-of-arrival estimation of coherent signals,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, no. 4, pp. 806–811 (1985) and S. U. Pillai and B. H. Kwon, “Forward/backward spatial smoothing techniques for coherent signals identification,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 1, pp. 8–15 (1989)).
In the subspace-based method for estimating the directions-of-arrival of uncorrelated signals, first an array covariance matrix is estimated from the noisy received array data, and then a signal subspace and a noise subspace are obtained through the eigenvalue decomposition (EVD) of this array covariance matrix. Thereafter, the orthogonality between the signal subspace and the noise subspace is exploited to estimate the directions-of-arrival of the incident signals. On the other hand, for the estimation of the directions-of-arrival of correlated signals (including signals with full correlation, i.e., coherent signals), in order to suppress the correlation among the incoming signals, an antenna having M array elements arranged in different spatial locations along a straight line at the same adjacent spacing (hereinafter, such an antenna may be referred to as a uniform linear array (ULA)) is divided into overlapping subarrays and then the covariance matrices of the subarrays are averaged to restore the number of dimensions of the signal subspace of the spatially averaged covariance matrix to the number of incident signals. Thus, the orthogonal relationship between the signal subspace and the noise subspace can be exploited to estimate the directions-of-arrival of correlated signals in the same manner as the subspace-based method for estimating the directions-of-arrival of uncorrelated signals.
Details of the spatial smoothing based MUSIC method for estimating the directions-of-arrival of coherent signals proposed in S. U. Pillai and B. H. Kwon, “Forward/backward spatial smoothing techniques for coherent signals identification,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 1, pp. 8–15 (1989) is described as follows.
Now, suppose that p narrow-band signals {si(k)} are incident upon a uniform linear array (ULA) along the angles {(θi}. If Ts denotes the sampling intervals, a signal received by each element is written as Equation (1).y(k)=[Y1(k), y2(k), . . . , yM(k)]T=A(θ(k))s(t)+w(k)A[a(θ1(k)), a(θ2(k)), . . . , a(θp(k))]a(θi(k))[1, ejω0τ(θi(k)), . . . , ejω0(M−1)τ(θi(k))]Ts(k)=[s1(k), s2(k), . . . , sp(k)]Tw(k)=[w1(k), w2(k), . . . , wM(k)]Tω0=2πf0, τ(θi(k))(d/c)sin θi(k)  (1)where fo, c, and d indicate the carrier frequency and propagation speed of the carrier wave, and the element interval (half-wave length), respectively. (•)T denotes transposition, and a(θi(k)) and A correspond to the array response vector and matrix, respectively. wi(k) indicates the spatially and temporally uncorrelated complex white Gaussian noise with zero-mean and variance σ2.
First, we consider the case that the directions-of-arrival of signals are constant over time, i.e., θi(k)=θi. In this case, an array covariance matrix is written as Equation (2).RE{y(k)yH(k)}=ARsAH+σ2IM  (2)where E{•} and (•)H indicate expectation operation and complex conjugate transposition respectively, Rs=E{S(k)SH(k)} is a covariance matrix of the incident signals, and IM is an M×M identity matrix. Furthermore, if the correlation rim between the received data yi(k) and ym(k) is defined as rim=E{yi(k)y*m(k)}, a relationship rim=r*mi holds, where (•)* denotes a complex conjugate. The array covariance matrix R in Equation (2) can be definitely represented as Equation (3).
                    R        =                  [                                                                      r                  11                                                                              r                  12                                                            ⋯                                                              r                                      1                    ⁢                    M                                                                                                                        r                  21                                                                              r                  22                                                            ⋯                                                              r                                      2                    ⁢                    M                                                                                                      ⋮                                            ⋮                                            ⋰                                            ⋮                                                                                      r                                      M                    ⁢                                                                                  ⁢                    1                                                                                                r                                      M                    ⁢                                                                                  ⁢                    2                                                                              ⋯                                                              r                  MM                                                              ]                                    (        3        )            
In order to estimate the directions-of-arrival {θk} of coherent signals, the spatial smoothing based MUSIC method divides the entire array into L overlapping subarrays each of which includes m (1≦m≦M) elements.
FIG. 14 is a diagram depicting subarrays in a uniform linear array (ULA).
As shown in FIG. 14, an array antenna 100 is composed of M antenna elements 101 arranged at the same adjacent spacing d, and is divided into L overlapping subarrays. In this structure, m and L are referred to as the subarray size and the number of subarrays, respectively, where a relationship L=M−m+1 holds. From Equation (1), the received vector yl(k) of the l-th subarray is given by Equation (4).yl(k)=[Yl(k),yl+1(k), . . . , yl+M−1(k)]T =Am Dl−1s(k)+wl(k)Am=[am(θ1),am(θ2), . . . , am(θp)]am(θi)=[1,ejω0τ(θi), . . . , ejω0(m−1)τ(θi)]Twl(k)=[wl(k),wl+1(k), . . . , wl−m+1(k)]T  (4)                where D is a diagonal matrix including ejω0τ(θ1), ejω0τ(θ2), . . . , ejω0(m−1)τ(θp) as elements, and l=1, 2, . . . , L.        
Furthermore, am(θi) and Am denote the response vector and matrix of the subarray, respectively. Therefore, a covariance matrix of the subarray is given by Equation (5).Rl=E{yl(k)ylH(k)}=AmDl−1Rs(Dl−1)HAmH+σ2Im  (5)
Furthermore, a covariance matrix given in Equation (6) is obtained by spatially averaging the covariance matrices {Rl} of the L subarrays in (5).
                              R          _                ⁢                                  =                              1            L                    ⁢                                    ∑                              l                =                1                            L                        ⁢                          R              l                                                          (        6        )            
Then the eigenvalue decomposition (EVD) of this spatially averaged covariance matrix R can be written as Equation (7).
                              R          _                ⁢                                  =                                            ∑                              i                =                1                            m                        ⁢                                          λ                i                            ⁢                              e                i                            ⁢                              e                i                H                                              =                      E            ⁢                                                  ⁢            Λ            ⁢                                                  ⁢                          E              H                                                          (        7        )            where ei and λi indicate an eigenvector and an eigenvalue, respectively, E is a matrix with columns {ei}, and Λ is a diagonal matrix with elements {λi}. Furthermore, the spaces spanned by a signal vector {e1, e2, . . . , ep} and a noise vector {ep+1, ep+2, . . . , em} are referred to as the signal subspace and the noise subspace, respectively. The signal subspace can be represented by using an array response vector. A direction-of-arrival estimation method based on the orthogonal relationship between the signal subspace and the noise subspace is called a subspace-based method.
From the eigenvalue analysis of the covariance matrix in Equation (7), an orthogonal relationship defined by Equation (8) is established between the noise vector {ep+1, ep+2, . . . , em} and the response vector am(θi) of the subarray belongs in the signal subspace.ekHam(θi)=0  (8)where k=p+1, . . . , m. From this orthogonal relationship, a spectrum Pssmusic(θ) written as Equation (9) can be calculated.
                                                                        P                _                            ⁢                                                                    ssmusic                    ⁢                      (            θ            )                          =                  1                                    ∑                              k                =                                  p                  +                  1                                            m                        ⁢                                                                                                e                    k                    H                                    ⁢                                                            a                      m                                        ⁡                                          (                      θ                      )                                                                                                  2                                                          (        9        )            where am(θ)=[1, ejωOτ(θ), . . . , ejωO(m−1)τ(θ)]T. In the spatial smoothing based MUSIC method, the directions-of-arrival of incoming signals are estimated from the locations of the highest p peaks of the spectrum given by Equation (9).
As shown in Equation (7), the subspace-based methods (including the (spatial smoothing) MUSIC) require the EVD of the array covariance matrix to obtain the signal subspace or the noise subspace for estimating the directions-of-arrival. In some practical applications, however, particularly if the number of array elements is large, the EVD or singular value decomposition (SVD) is complicated and time-consuming when the estimation of the time-varying directions of incident signals should be carried out in a real-time manner. Therefore, applications of the subspace-based direction-of-arrival estimation methods are limited by the eigendecomposition (EVD or SVD) due to the computationally intensive eigendecomposition processing. In many cases of a practical mobile communication system, since the signals from a calling party (mobile terminal) arrive at the array antenna in a base-station via the direct path and reflection paths resulting from signal reflection at objects such as buildings, the technique for estimating the directions-of-arrival of coherent signals in a multipath propagation environment plays an important role. In the above-described direction estimation methods, however, since the desired signals cannot be distinguished from interfering signals, the directions-of-arrival of all signals must be calculated. Thus, to process many incoming waves, it is necessary to use many elements in the array antenna. This leads to an increase in size and cost associated with the array antenna. Furthermore, if the directions-of-arrival of desired signals vary over time due to, for example, the movement of the calling party (signal source), then the directions of the signals impinging on the array cannot be estimated at high speed and with high accuracy by using the ordinary subspace-based methods or the accurate reception and transmission beams cannot be formed at the base-station. This causes the performance of the receiving and transmission system at the base-station to deteriorate.
Recently, adaptive direction-of-arrival estimation and tracking methods without eigendecomposition have been studied, such as the adaptive subspace-based methods without eigendecomposition (SWEDE) (refer to, for example, A. Eriksson, P. Stoica, and T. Söderström, “On-line subspace algorithms for tracking moving sources,” IEEE Trans. Signal Processing, vol. 42, no. 9, pp. 2319–2330 (1994)). These methods, however, exhibit significantly degraded performance in the case of coherent signals, low signal-to-noise ratio (SNR), or a small number of snapshots. Furthermore, the least squares (LS) technique involved in the SWEDE requires a high degree of computational complexity.
The present inventor proposed a direction-of-arrival estimation and tracking method based on the cyclostationarity of communication signals (refer to, for example, J. Xin and A. Sano, “Directions-of-arrival tracking of coherent cyclostationary signals in array processing,” IEICE Trans. Fundamentals, vol. E86-A, no. 8, pp. 2037–2046 (2003)). This method using the LS technique, however, requires considerably large length of array data because it exploits a temporal property known as the cyclostationarity of incident signals.
The present inventor also proposed a direction-of-arrival estimation method called subspace-based method without eigendecomposition (SUMWE), which does not need the eigendecomposition and is computationally efficient (refer to, for example, J. Xin and A. Sano, “Computationally efficient subspace-based method for direction-of-arrival estimation without eigendecomposition,” IEEE Trans. Signal Processing, vol. 52, no. 4, pp. 876–893 (2004)). This method, however, does not take into consideration the issues of online direction-of-arrival estimation and time-varying direction-of-arrival tracking.
To handle these issues of adaptive direction-of-arrival estimation and time-varying direction-of-arrival tracking, the present inventor has proposed an adaptive direction-of-arrival estimation and tracking method called the adaptive bearing estimation and tracking (ABEST) technique exploiting the computationally efficient SUMWE technique (refer to, for example, J. Xin, Y. Ohashi, and A. Sano, “Efficient subspace-based algorithms for adaptive direction estimation and tracking of narrowband signals in array processing,” Proc. IFAC 8th Workshop on Adaptation and Learning in Control and Signal Processing (ALCOSP' 04), pp. 535–540, Yokohama, Japan, (2004)).
The aforementioned methods for tracking the directions-of-arrival of radio waves, however, cannot accurately track the crossing directions of coherents signals, where the trajectories of the directions of incident signals intersect with one another due to the movement of the signal source (such as a calling party).